Factorisation of Lefschetz zeta functions and twisted periodic orbits
Let \(x\) be a periodic point of period \(n\) for a diffeomorphism \(f\) of a compact manifold. Denote by \(E^ u_ x\) the frame spanned by the eigenvectors of \(Df^ n(x)\) that correspond to the eigenvalues \(\lambda\) with \(| \lambda | > 1\). The point \(x\) is called twisted if \(Df^ n(x)\) reverses the orientation of \(E^ u_ x\). The author constructs a new factorization of the Lefschetz zeta function for \(f\) and studies its connection with the existence of twisted periodic orbits (t.p.o. below). For example, for a surface diffeomorphism conditions are given under which the existence of one t.p.o. implies the existence of a countable family of t.p.o.
scientific article; zbMATH DE number 704941
scientific article